the grunt that gives you the lift key is in a room with one other grunt and when you beat him in a battle he drops it. to get to him go to the second floor (or the first I can't remember and i did yeasterday hahahahaha) get through the maze with the arrow switches and go up or down the stairs (which ever direction they're going and battle the one in the back of the room. If it is not him the on the first floor on the other side of that gate thingy is the lift key.
sorry if you can't understand it. just leave me a message on my message board and I will make it more clear.
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A rocket grunt drops the key on B3.
You can find the Lift Key in the Team Rocket Hideout on Pokemon FireRed. It is dropped by a Grunt on basement floor 4 after defeating him.
In Basement Floor 3 there is a Rocket Grunt standing in the corner of the room, battle him and he will drop the Lift Key. If the key doesn't appear right away move away from the Rocket and the item will appear.
They're in the Underground, in the lower part that branches off. You go through the door that used to be locked. but first you have to defeat ever sngle team rocket grunt to get card key to open door
You get the Lift Key on B4F when you battle a Team Rocket Grunt in the far north corner. He even says "Who has the Lift Key" before the battle begins. He has a Level 21 Zubat and Koffing. Once you defeat him, then he will drop the key.